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Recent data on superflares on sun-like stars and radiocarbon data on solaractivity in the past are both indicative of transient epochs of unusually highmagnetic activity. We propose an explanation for the grand activity maxima inthe framework of a solar dynamo model with fluctuating parameters. Solar-typedynamos are oscillatory because of the combination of the solar-typedifferential rotation with positive (in the Northern hemisphere) alpha-effect.An artificial reversal of the sign in the alpha-effect changes the dynamo to asteady regime with hundreds of times larger magnetic energy compared to theamplitude of the cyclic dynamo. Sufficiently large and durable fluctuationsreversing the sign of the alpha-effect during the growth phase of a magneticcycle can, therefore, cause a transient change to a steady dynamo withconsiderably increased magnetic energy. This qualitative scenario for grandactivity maxima is supported by computations of the dynamo model with afluctuating alpha-effect. The computed statistics of several thousand magneticcycles gives examples of cycles with very high magnetic energy. Our preliminaryestimations, however, suggest that the probability of solar superflares isextremely low.

Dynamo model for grand maxima of solar activity: can superflares occur on the Sun?